M. Mirzaei

activity

20182020

most citedConstructions of point-line arrangements in the plane with large girth

1 citations · 2 across the 3 of their papers we have counts for

collaborators

Showing math.COShow all

4 papers · 1 filter

math.CO2019★ 1 cited

Constructions of point-line arrangements in the plane with large girth

Mozhgan Mirzaei, Andrew Suk, Jacques Verstraëte

A classical result by Erdős, and later on by Bondy and Simonivits, states that every $n$ -vertex graph with no cycle of length $2 k$ has at most $O (n^{1 + 1/ k})$ edges. This bound is…

math.CO2018

On grids in point-line arrangements in the plane

Mozhgan Mirzaei, Andrew Suk

The famous Szemerédi-Trotter theorem states that any arrangement of $n$ points and $n$ lines in the plane determines $O (n^{4/3})$ incidences, and this bound is tight. In this paper…

math.CO2018

A note on conditional expanders over prime fields

Mozhgan Mirzaei

Let $F_{p}$ be a prime field of order $p,$ and $A$ be a set in $F_{p}$ with $∣ A ∣ \leq p^{1/2} .$ In this note, we show that \[\max\{|A+A|, |f(A, A)|\}\gtrsim |A|^{\fra…

math.CO2018

A positive fraction mutually avoiding sets theorem

Mozhgan Mirzaei, Andrew Suk

Two sets $A$ and $B$ of points in the plane are \emph{mutually avoiding} if no line generated by any two points in $A$ intersects the convex hull of $B$ , and vice versa. In 1994, A…